Question: Integrate. $ \int -7\sin(x)\,dx $ $=$ $+ C$
We need a function whose derivative is $-7\sin(x)$. We know that the derivative of $\cos(x)$ is $-\sin(x)$, so let's start there: $\dfrac{d}{dx} \cos(x) = -\sin(x)$ Now let's multiply by $7$ : $\dfrac{d}{dx}\left[ 7\cos(x) \right]= -7\sin(x)$ Because finding the integral is the opposite of taking the derivative, this means that: $ \int -7\sin(x)\,dx =7 \cos(x)\, + C$ The answer: $7 \cos(x)\, + C$